Test Your Calculus Knowledge Take this quiz to see how well you understand the concepts and principles of calculus. michelle published on September 08, 20231 response 0 « Previous Next » Questions in vertical order 1/12 What is the limit of the function f(x) = 3x^2 + 5x - 2 as x approaches 2? 9 19 -19 17 2/12 What is the derivative of the function f(x) = 4x^3 - 2x^2 + 5x - 3? 12x^2 - 4x + 5 12x^2 - 4x + 1 12x^2 - 4x + 6 12x^2 - 4x - 2 3/12 What is the integral of the function f(x) = 2x^2 + 3x + 1? 2/3x^3 + 3/2x^2 + x 3/4x^3 + 4/3x^2 + x 3/5x^3 + x^2 + x 2/5x^3 + 2/3x^2 + x 4/12 What is the product rule in calculus used for? Differentiating a product of two functions Finding the limit of a function Integrating a function Differentiating a quotient of two functions 5/12 Which theorem in calculus states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a)? Fundamental Theorem of Calculus Mean Value Theorem Intermediate Value Theorem L'Hopital's Rule 6/12 Which of the following functions is not a transcendental function? Sin(x) e^x log(x) x^2 7/12 What is the area bounded by the region under the curve y = x^2 from x = 0 to x = 2? 1/3 4/3 16/3 8/3 8/12 What is the second derivative of the function f(x) = 3x^4 - 4x^3 + 2? 12x^3 - 12x^2 12x^3 - 12x^2 + 2 6x^3 - 6x^2 6x^3 - 6x^2 + 2 9/12 What is the limit of (sin x)/x as x approaches 0? 1 0 undefined infinity 10/12 What is the area bounded by the region under the curve y = sqrt(x) from x = 0 to x = 4? 4 8 16 2 11/12 What is the derivative of the function f(x) = ln(x^2 + 1)? (2x)/(x^2 + 1) (2x^2)/(x^2 + 1) (2x^3)/(x^2 + 1) (2x^4)/(x^2 + 1) 12/12 What is the critical point of the function f(x) = 3x^3 - 4x^2 + 2x - 5? 1 2 -2 4/3
